The interplay between the injection spectrum from the accelerator and the rigidity dependence of the escape time from the environment, \(\tau _{\rm esc}(R)\) , governs the energy dependence of the number of interactions before escape, as was noted in equation (4) of [1]}. There, the focus was on how the high-pass filter mechanism creates the ankle in the UHECR spectrum and produces the observed light extragalactic UHECRs below the ankle. As noted in [1]}, this mechanism leads to a hardening of the escaping CR spectrum. Thus the Auger combined fit to the spectrum and composition [3]} favoring an \(\sim E^{-1}\)  or harder spectrum escaping the source, does not necessarily mean that the accelerator produces such a hard spectrum. In principle, the fundamental spectrum from the accelerator could be much softer, e.g., \(\sim E^{-2}\)  as predicted by diffusive shock acceleration, with the low-energy component of any given \(A\)  being more depleted through interactions because of their longer residence time in the environment – thus hardening the escaping spectrum for each composition.An alternative mechanism to harden the accelerated spectrum is through magnetic suppression of the spectrum at low-ridigities due to the horizon induced by the extragalactic magnetic field [4]}, [5]}.
